Reactive Control and its Operation Limits in Responding to a Novel Slip in Gait

Abstract

The purposes of this study were: (1) to examine the reactive control of the resultant joint moments at the lower limbs in response to a novel and unannounced slip; (2) to establish individualized forward-dynamics models; and (3) to explore personal potential by determining the operation limits of these moments at each lower limb joint, beyond which the resulting motion at this or other joints will exceed its/their normal range(s). Ten young subjects’ kinematics and kinetics, collected during regular walking and during their first exposure to a novel and unannounced slip, were randomly selected from an existing database. An inverse-dynamics approach was applied to derive their (original) resultant joint moments, which were then used as input to establish forward-dynamics models, each including an individualized 16-element foot model to simulate ground reaction force. A simulated annealing (SA) algorithm was applied to modify the original moments, so that the subsequent output (baseline) moments can closely reproduce these subjects’ recorded motion. A systematic alteration of the baseline moments was employed to determine the operation limits. The results revealed that the subjects reactively increased the hip extensor and knee flexor moments and reduced their ankle plantar flexor moments of their single-stance limb following slip onset. The “baseline” correction of the original moments can reach as much as 21% of the original moments. The analysis of the operation limits revealed that these individuals may be able to further increase their knee flexors more so than increase the hip extensors or reduce ankle plantar flexors before causing abnormal joint movement. Such systematic approach opens the possibility to properly assess an individual’s rehabilitation potential, and to identify whether this person’s strength is the limiting factor for stability training.

Appendix: The Optimization Procedure

Each joint activation level time history was divided into a set of independent, linearly interpolated variables or control nodes. The initiation of the control nodes for SA was the original joint moments derived from the inverse-dynamics analysis. Once the control nodes were determined, each joint moment history was reconstructed using linear interpolation (Eq. (2)). After the initiation, the forward-dynamics simulation was performed by integrating the equations of motion (Eq. (1)). The objective function (Eq. (3)) was then evaluated by comparing the output kinematics with the corresponding experimental values. Based on the evaluation, the values of control nodes and spring/damping coefficient of the visco-elastic element would be adjusted by SA in light of its acceptance/rejection criteria. This iteration was continued until the improvement in the object function became <10⁻³ for 500 consecutive function evaluations. The optimization-derived joint moments were the baseline moments used to investigate the operation limits.